CN105548783B - Ultrahigh-voltage alternating-current transmission line with four-circuit on single tower Zero sequence parameter accurate measurement method - Google Patents
Ultrahigh-voltage alternating-current transmission line with four-circuit on single tower Zero sequence parameter accurate measurement method Download PDFInfo
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Abstract
The invention discloses a kind of novel ultrahigh pressure transmission line with four-circuit on single tower Zero sequence parameter accurate measurement methods.The residual voltage and zero-sequence current for measuring four back transmission line head and ends simultaneously, utilize GPS（GPS）Sync identification function, realize to the synchronized sampling of residual voltage and zero-sequence current；Utilize the super-pressure transmission line with four-circuit on single tower model based on distributed constant, corresponding differential equation group is obtained, then the measurement method provided by this patent obtains the zero sequence resistance of super-pressure transmission line with four-circuit on single tower, zero sequence inductance, zero sequence capacitance parameter with computational methods.The method of the present invention is based on distributed parameter model, is therefore particularly suited for handing over over long distances（Directly）The parameter measurement for flowing transmission line of electricity, can be greatly improved measurement accuracy, can meet the needs of Practical Project measurement.
Description
Technical field
It is same more particularly, to a kind of ultrahigh-voltage alternating-current the present invention relates to a kind of power transmission line zero-sequence parameter accurate measurement method
Four back transmission line Zero sequence parameter accurate measurement method of tower.
Background technology
Transmission line of electricity is the important component of electric system, plays the important function of electrical energy transportation.Transmission line parameter
It is the basic data of many electric system relative programs, especially has in relay protection setting and fault location highly important
Using.High-precision transmission line parameter data are obtained, contribute to the Load flow calculation and short circuit calculation of electric system, this is for electricity
The safe and stable operation of Force system has particularly important meaning.
Power transmission line zero-sequence parameter is highly prone to the influence of external environment, such as transmission of electricity thread geometry, electric current, environment temperature
The factors such as degree, wind speed, soil resistivity, lightning conducter erection mode and line route.Simultaneously as zero sequence circuit is through too greatly,
And depth of the loop current in the earth is difficult accurately to measure, theoretical calculation usually has ignored the influence of these factors, therefore according to
The exact value of circuit Zero sequence parameter cannot be obtained by theoretical calculation.Therefore, the relevant regulation regulation in China, power transmission line zero-sequence ginseng
Number must survey.
With the continuous development of electric system, transmission line of electricity needs to have the ability of the electrical energy transportation of more capacity, tradition
Multiple-circuit on same tower be unable to meet demand in certain situations, developed on this basis super-pressure with tower four feed back power technology.
Super-pressure quadri-circuit lines on the same tower road has the advantages of saving transmission of electricity corridor, reducing shaft tower construction and electric power transportation cost, in reality
It gets application in the engineering of border.But since extra high voltage network distance, coupling parameter are more, the accurate measurement band of line parameter circuit value is given
Great difficulty is carried out.
The research of transmission line with four-circuit on single tower zero sequence parameter measurement has been achieved for some achievements at present, predominantly using dry
It disturbs method, method of addition, alien frequencies method to measure, ignores the influence of distribution capacity, may be only available for short haul circuits parameter measurement.And it is previous
The zero sequence parameter measurement method derived using distributed parameter model and equation for transmission line, cannot measure zero sequence mutual resistance parameter, and
The mutual parameter of four loop line road zero sequence capacitances and zero sequence inductance being also assumed to be respectively equal so that parameter measurement error is very big,
It cannot be satisfied Practical Project measurement demand.
Invention content
The present invention is mainly to solve can not be used due to ignoring distribution capacity using lumped parameter present in the prior art
In (300km or more) transmission line parameter measures over long distances the drawbacks of, previous measurement method is also avoided due to parameter excessively
The technical issues of simplifying the defect for causing measurement error excessive；Provide a kind of super-pressure short distance Zero sequence parameter of being not only suitable for
It measures, is also applied for long distance transmission line zero sequence parameter measurement；Solves sex chromosome mosaicism while strange land signal measurement measures；It can
Disposably measure zero sequence resistance, zero sequence inductance, zero sequence capacitance parameter.
The above-mentioned technical problem of the present invention is mainly to be addressed by following technical proposals：
A kind of ultrahigh-voltage alternating-current transmission line with four-circuit on single tower Zero sequence parameter accurate measurement method, which is characterized in that definition is same
Four back transmission line of tower includes circuit a, circuit b, circuit c and circuit d, wherein
Rule one：The zero sequence self-impedance of circuit a and circuit b is identical, is Z11, the zero sequence self-impedance phase of circuit c and circuit d
Together, it is Z22, the zero sequence mutual impedance parameter between circuit a and circuit b is Zab；Zero sequence mutual impedance between circuit a and circuit c
Zero sequence mutual impedance parameter between parameter and circuit b and circuit d is identical, is Zac；Zero sequence mutual resistance between circuit a and circuit d
Zero sequence mutual impedance parameter between anti-parameter and circuit b and circuit c is identical, is Zad；Zero sequence between circuit c and circuit d is mutual
Impedance parameter is Zcd；
Rule two：The zero sequence of circuit a and circuit b is identical from susceptance, is Y11, the zero sequence of circuit c and circuit d is from susceptance phase
Together, it is Y22, the mutual susceptance parameter of zero sequence between circuit a and circuit b is Yab；The mutual susceptance of zero sequence between circuit a and circuit c
The mutual susceptance parameter of zero sequence between parameter and circuit b and circuit d is identical, is Yac；Zero sequence between circuit a and circuit d is mutually electric
The mutual susceptance parameter of zero sequence received between parameter and circuit b and circuit c is identical, is Yad；Zero sequence between circuit c and circuit d is mutual
Susceptance parameter is Ycd；
Measuring process includes：
Step 1, have a power failure and measure transmission line with four-circuit on single tower, four loop line road first and last end three-phases are distinguished into short circuit；Route survey
Including：
Measurement method one：Circuit a head ends pressurize, end ground connection；Circuit b head ends are hanging, end ground connection；Circuit c head ends are outstanding
Sky, end ground connection；Circuit d head ends are hanging, end ground connection；
Measurement method two：Circuit a head ends are hanging, end ground connection；Circuit b head ends are hanging, end ground connection；Circuit c head ends add
Pressure, end ground connection；Circuit d head ends are hanging, end ground connection；
Step 2, using the sync identification function of GPS, synchro measure circuit a, circuit b, circuit c and
The residual voltage data and zero-sequence current data of circuit d head ends and end；
Step 3, the residual voltage measurement data and zero-sequence current that are obtained under each independent measurement method obtained by step 2 are surveyed
Data are measured, the zero sequence fundamental voltage phasor and zero sequence base of head end and end under the independent measurement method are obtained using fourier algorithm
Wave electric current phasor recycles these phasor datas to solve the Zero sequence parameter of transmission line with four-circuit on single tower to come；
The parameter of required solution includes the zero sequence self-impedance parameter Z of unit length11、Z22, zero sequence mutual impedance parameter Zab、Zac、
Zad、Zcd, zero sequence is from susceptance parameter Y11、Y22, the mutual susceptance parameter Y of zero sequenceab、Yac、Yad、Ycd, then solved according to following two formula
All Zero sequence parameters：
Wherein, because the leakage current very little of circuit, does not consider conductance parameter；Quadri-circuit lines on the same tower road is defined as parallel
It sets up and length is all l, the zero sequence fundamental voltage phasor for defining tetra- back transmission line head end of a, b, c, d is respectively The zero sequence fundamental voltage phasor of end is respectivelyThe zero sequence fundamental wave electricity of head end
Flowing phasor is respectivelyThe zero sequence fundamental current phasor of end is respectively
Zero sequence parameter solution procedure is as follows：
Step 3.1, by Zero sequence parameter Z11、Z22、Zab、Zac、Zad、ZcdAnd Y11、Y22、Yab、Yac、Yad、YcdObtain power transmission line
The relationship of road first and last terminal voltage electric current：
Wherein, Aaa,Aab,Aba,Abb, Baa,Bab,Bba,Bbb,A′aa,A′ab,A′ba,Abb, B 'aa,B′ab,B′ba,B′bbBe with
The related intermediate variable of line parameter circuit value；
Step 3.2, intermediate variable A is calculated by two kinds of measurement methods in step 1aa,Aab, Aba, A, Baa,Bab,Bba,
Bbb,A′aa,A′ab,A′ba,A′bb, B 'aa,B′ab,B′ba,B′bb：
In the above formulas, voltage phasor or electric current phasor with subscript " 1 " or " 2 " indicate that the phasor is connections side
The zero sequence fundamental voltage phasor or zero sequence fundamental wave electricity that measurement data under formula 1 or the mode of connection 2 is calculated through Fourier algorithm
Flow phasor；
Step 3.3, characteristic root p is calculated according to following formula1,p2,p1′,p′2；
Then pass through p1,p2,p1′,p′2Solve A1,A2,B1,B2And A1′,A′2,B1′,B′2；
Step 3.4, by Aaa,Aab,Aba,Abb,A′aa,A′ab,A′ba,A′bbSubstitute into following formula calculating matrix T1And T3；
Step 3.5, B is substituted intoaa,Bab,Bba,Bbb,B′aa,B′ab,B′ba,B′bbWith matrix T1、T3Computing impedance matrix Z1With
Z2；
Step 3.6 is by matrix T1、T3、Z1、Z2Following formula is substituted into, zero sequence admittance matrix is calculated；
Step 3.7, zero sequence impedance and zero sequence admittance parameter are calculated；
Finally, by Z11、Z22、Zab、Zac、Zad、ZcdAnd Y11、Y22、Yab、Yac、Yad、YcdIt obtains corresponding same tower four and feeds back electricity
Circuit zero sequence resistance, zero sequence inductance, zero sequence capacitance parameter；
Wherein, symbol sh () indicates that hyperbolic sine function, symbol ch () indicate hyperbolic cosine function, symbol arch
() indicates that Inverse Hyperbolic Cosine Function, the π of ω=2 f, f are power system frequency 50Hz, and l indicates quadri-circuit lines on the same tower road length.
The invention has the advantages that：1, be not only suitable for the measurement of super-pressure short distance Zero sequence parameter, be also applied for it is long away from
From power transmission line zero-sequence parameter measurement；2, the method for the present invention is measured solves the same of strange land signal measurement measurement using GPS technology
When sex chromosome mosaicism；3, zero sequence resistance, zero sequence inductance, zero sequence capacitance parameter can disposably be measured, and measurement accuracy is not less than only surveying
Measure the measurement method of one of which Zero sequence parameter.
Description of the drawings
Attached drawing 1 is super-pressure transmission line with four-circuit on single tower equivalent schematic.
Attached drawing 2 is the distributed parameter model schematic diagram of super-pressure transmission line with four-circuit on single tower.
Attached drawing 3 is super-pressure transmission line with four-circuit on single tower spatial position floor map.
Attached drawing 4 is the method for the present invention and conventional method resistance error comparison diagram.
Attached drawing 5 is the method for the present invention and conventional method inductance error comparison diagram.
Attached drawing 6 is the method for the present invention and conventional method capacitance error comparison diagram.
Attached drawing 7 is the power transmission line zero-sequence resistance measurement error and transmission line length relational graph that present invention measurement obtains.
Attached drawing 8 is the power transmission line zero-sequence inductance measurement error and transmission line length relational graph that present invention measurement obtains.
Attached drawing 9 is the power transmission line zero-sequence capacitance measurement error and transmission line length relational graph that present invention measurement obtains.
Specific implementation mode
Below with reference to the embodiments and with reference to the accompanying drawing the technical solutions of the present invention will be further described.
Embodiment：
Below in conjunction with drawings and examples the present invention will be described in detail technical solution, the present invention includes the following steps：
Step 1, selection have a power failure measure transmission line with four-circuit on single tower, the transmission line with four-circuit on single tower by circuit a, circuit b,
Circuit c and circuit d compositions.
Transmission line with four-circuit on single tower Zero sequence parameter is measured using following two independent measurement methods：
(1) circuit a head ends three-phase short circuit applies single-phase voltage, end three-phase short circuit ground connection；Circuit b head end three-phase short circuits
Vacantly, three-phase short circuit in end is grounded；Circuit c head end three-phase short circuits are grounded, end three-phase short circuit ground connection；Circuit d head end three-phases are short
Ground connection, end three-phase short circuit ground connection；
(2) circuit a head ends three-phase short circuit is hanging, end three-phase short circuit ground connection；Circuit b head end three-phase short circuits are hanging, end
Three-phase short circuit is grounded；Circuit c head end three-phase short circuits apply single-phase voltage, end three-phase short circuit ground connection；Circuit d head end three-phases are short
Connect hanging, end three-phase short circuit ground connection；
Step 2, it is measured respectively using the selected various independent modes of step 1, utilizes the same of GPS
Walk timing function, synchro measure circuit a, circuit b, circuit c and circuit d first and ends residual voltage data and zero-sequence current number
According to；
The time reference that error is less than 1 microsecond is obtained using the timing function of GPS, in the case where GPS time synchronizes, embodiment is same
When acquire four back transmission line head and ends residual voltage and transmission line of electricity head and end zero-sequence current, and with the side of file
Formula preserves measurement data.
Step 3, the residual voltage measurement data and zero-sequence current that are obtained under each independent measurement method obtained by step 2 are surveyed
Data are measured, the zero sequence fundamental voltage phasor and zero sequence base of head end and end under the independent measurement method are obtained using fourier algorithm
Wave electric current phasor recycles these vector datas to solve the Zero sequence parameter of transmission line with four-circuit on single tower to come.
Embodiment independent is measured various by after being measured under the various independent measurement methods selected in step 1
The file that gained measurement data preserves under mode is aggregated into a computer, and under each independent measurement method, first and last end is equal
After the pressurization of line taking road in some time (such as between 0.2 second to 0.4 second) measurement data, respectively obtained respectively using fourier algorithm
The zero sequence fundamental voltage phasor of transmission line of electricity head and end and zero sequence fundamental current phasor, then carry out under a independent measurement method
Zero sequence parameter solves.Fourier algorithm is the prior art, and it will not go into details by the present invention.
Transmission line with four-circuit on single tower coupling parameter is more, must be to Zero sequence parameter to avoid the problem that parameter can not excessively solve
Make certain simplification.
If the i-th loop line road unit length zero sequence self-resistance, zero sequence self-inductance, zero sequence self-capacitance, zero sequence self-impedance and zero sequence
It is respectively R from susceptancei、Li、Ci、ZiAnd Yi.If zero sequence mutual resistance, zero sequence mutual inductance, zero sequence are mutual between i-th time and jth loop line road
Capacitance, zero sequence mutual impedance and the mutual susceptance of zero sequence are respectively Rij、Lij、Cij、ZijAnd Yij.And there is Zi=Ri+jwLi, Zij=Rij+
jwLij, Yi=jwCi, Yij=jwCij.Zero sequence resistance and zero sequence inductance parameters are converted to zero-sequence impedance parameter, by zero sequence capacitance
Parameter is converted into zero sequence susceptance parameter.
Referring to attached drawing 1, since transmission line with four-circuit on single tower uses symmetric form tower, and per back transmission line three-phase transposition, then
Have：Za=Zb, Zc=Zd, Zac=Zbd, Zad=Zbc.For zero sequence susceptance parameter, equally there is Ya=Yb, Yc=Yd, Yac=Ybd, Yad
=Ybc。
Therefore after simplifying, obtain needing the Zero sequence parameter solved including zero sequence self-impedance parameter Z11、Z22, zero sequence mutual impedance
Parameter Zab、Zac、Zad、Zcd, zero sequence is from susceptance parameter Y11、Y22, the mutual susceptance parameter Y of zero sequenceab、Yac、Yad、Ycd。
Zero sequence resistance, zero sequence inductance, zero sequence capacitance computational methods are derived using above-mentioned simplified Zero sequence parameter, avoid parameter
The problem of can not excessively solving, while also avoiding leading to calculate the larger problem of error since parameter excessively simplifies.Above-mentioned letter
Change the key property that Zero sequence parameter remains quadri-circuit lines on the same tower road Zero sequence parameter, ensure that the reasonability of result of calculation.
Voltage unit in the present invention is all volt, and current unit is all ampere.It is surveyed using each independent measurement method is lower
The four loop line road first and last end zero sequence fundamental voltage phasors and zero sequence electricity fundamental wave stream phasor obtained, can calculate intermediate variable, then pass through
Intermediate variable finds out the Zero sequence parameter of four back transmission lines.
The Zero sequence parameter solution procedure of embodiment double back transmission line is as follows：
Ignore do not consider herein due to conductance parameter very little referring to Fig. 2, as shown is based on simplified Zero sequence parameter
And length is l (units：Km same tower four) returns coupling power transmission line distributed parameter model.
One section of infinitesimal dx is taken at from line end x.A, it is first from the infinitesimal dx at line end x to feed back electric wire by b, c, d tetra-
Terminal voltage is respectivelyTerminal voltage is respectively Line current is respectively
Because the leakage current very little of circuit, does not consider conductance parameter.Quadri-circuit lines on the same tower road is defined as parallel erection
And length is all l, the zero sequence fundamental voltage phasor for defining tetra- back transmission line head end of a, b, c, d is respectively The zero sequence fundamental voltage phasor of end is respectivelyThe zero sequence fundamental current phasor of head end is distinguished
ForThe zero sequence fundamental current phasor of end is respectively
Zero sequence parameter solution procedure is as follows：
By Zero sequence parameter Z11、Z22、Zab、Zac、Zad、ZcdAnd Y11、Y22、Yab、Yac、Yad、YcdIt is as follows to obtain equation for transmission line：
Construct second order differential equations
Wherein：
Wherein, matrix α, β, ξ is the relevant constant matrices constructed needed for second order differential equations.
If the initial condition of the second order differential equations is：
f1(0)=aa, f2(0)=bb
Wherein, aa, bb, cc, dd are constant.
The Laplace transform under second order form is done to it, is obtained
Above formula is written as form, wherein I is second order unit matrix.
And calculating matrix s2The characteristic root of I- ξ：
det(s2I- ξ)=(s2-ξ11)(s2-ξ22)-ξ12ξ21 (A6)
=(s2-p1 2)(s2-p2 2)
Inverse Laplace transform is carried out to it to obtain
MatrixIt is intermediate variable related with matrix α and ξ with σ.
According to equation for transmission line, corresponding transformation is carried out to it and is obtained：
It differentiates to above four equation both sides, obtains four differential equation groups：
First differential equation group be：
The differential equation group has following initial condition：
Second differential equation group be
The differential equation group has following initial condition：
Third differential equation group is：
The differential equation group has following initial condition：
4th differential equation group be：
The differential equation group has following initial condition：
Wherein：
Above four differential equation groups (A12), (A13), (A14), (A13) and (A3) have identical form, therefore substitute into
(A7), and by head end voltage this is substituted into as a result, obtaining the relationship of first and last terminal voltage electric current：
Wherein：
Intermediate variable A is calculated by two kinds of measurement methodsaa,Aab,Aba,Abb, Baa,Bab,Bba,Bbb, A 'aa,A′ab,A′ba,
A′bb, B 'aa,B′ab,B′ba,B′bb：
Characteristic root p is calculated according to following formula1,p2,p′1,p′2；
Substitute into Aaa,Aab,Aba,Abb,A′aa,A′ab,A′ba,A′bbCalculating matrix T1And T3；
Substitute into Baa,Bab,Bba,Bbb,B′aa,B′ab,B′ba,B′bbWith matrix T1、T3Computing impedance matrix Z1、Z2；
Calculate zero sequence impedance and zero sequence admittance parameter；
Finally, by Z11、Z22、Zab、Zac、Zad、ZcdAnd Y11、Y22、Yab、Yac、Yad、YcdIt obtains corresponding same tower four and feeds back electricity
Circuit zero sequence resistance, zero sequence inductance, zero sequence capacitance parameter.
For the sake of effect in order to illustrate the present invention, by taking 500kV/220kV transmission line with four-circuit on single tower as an example.
The Zero sequence parameter on the quadri-circuit lines on the same tower road is measured with measurement method of the present invention, line length becomes from 100km to 900km
When change, for circuit zero sequence resistance, zero sequence inductance, zero sequence capacitance error always within 0.4%, the practical need of engineering can be met
It asks.And conventional method measurement Zero sequence parameter error is very big, worst error has reached 50%, therefore for long-distance transmission line
Road, conventional method cannot meet measurement accuracy requirement
When being changed from 100km to 900km to quadri-circuit lines on the same tower road length with technical solution of the present invention and traditional measurement method
Simulated measurement is carried out, measurement result is as shown in table 2 to table 7.
1 Zero sequence parameter theoretical value of table
The zero sequence resistance simulated measurement result that 2 measurement method of the present invention of table obtains
The zero sequence artificial inductive measurement result that 3 measurement method of the present invention of table obtains
The zero sequence capacitance simulated measurement result that 4 measurement method of the present invention of table obtains
The zero sequence resistance simulated measurement result that 5 conventional method of table obtains
The zero sequence artificial inductive measurement result that 6 conventional method of table obtains
The zero sequence capacitance simulated measurement result that 7 conventional method of table obtains
The Zero sequence parameter that Zero sequence parameter that measurement method provided by the present invention obtains is obtained with traditional measurement method into
Row comparison, from table 2 to table 7, Fig. 4 to Fig. 9 can be seen that when circuit is shorter (be less than 300km), the error of conventional method compared with
Small, because conventional method uses lumped parameter model, for short distance transmission line of electricity, distributed capacitor influence is very weak, therefore accidentally
Poor very little.But when line length increases, the error of conventional method significantly increases, wherein resistance error increases quickly, inductance
Take second place, capacitance error increases slower, but when circuit reaches 900km, error is very big, and worst error has reached 50%, this
Being in engineering cannot be received.And the method for the present invention has fully considered distribution capacity due to the use of distributed parameter model
It influences, therefore no matter circuit is long range or short distance, measurement error all very littles, wherein resistance error is within 0.4%, electricity
Error is felt within 0.2%, and capacitance error is within 0.3%.Simulation result shows that the method for the present invention measurement accuracy is apparently higher than
Traditional measurement method hands over the zero sequence parameter measurement of (straight) Flow Line in particular for long range, can meet wanting for engineering survey
It asks.
Specific embodiment described herein is only an example for the spirit of the invention.Technology belonging to the present invention is led
The technical staff in domain can make various modifications or additions to the described embodiments or replace by a similar method
In generation, however, it does not deviate from the spirit of the invention or beyond the scope of the appended claims.
Claims (1)
1. a kind of ultrahigh-voltage alternating-current transmission line with four-circuit on single tower Zero sequence parameter accurate measurement method, which is characterized in that define same tower
Four back transmission lines include circuit a, circuit b, circuit c and circuit d, wherein
Rule one：The zero sequence self-impedance of circuit a and circuit b is identical, is Z11, the zero sequence self-impedance of circuit c and circuit d is identical,
It is Z22, the zero sequence mutual impedance parameter between circuit a and circuit b is Zab；Zero sequence mutual impedance parameter between circuit a and circuit c
Zero sequence mutual impedance parameter between circuit b and circuit d is identical, is Zac；Zero sequence mutual impedance ginseng between circuit a and circuit d
Number is identical as the zero sequence mutual impedance parameter between circuit b and circuit c, is Zad；Zero sequence mutual impedance between circuit c and circuit d
Parameter is Zcd；
Rule two：The zero sequence of circuit a and circuit b is identical from susceptance, is Y11, the zero sequence of circuit c and circuit d is identical from susceptance,
It is Y22, the mutual susceptance parameter of zero sequence between circuit a and circuit b is Yab；The mutual susceptance parameter of zero sequence between circuit a and circuit c
The mutual susceptance parameter of zero sequence between circuit b and circuit d is identical, is Yac；The mutual susceptance ginseng of zero sequence between circuit a and circuit d
Number is identical as the mutual susceptance parameter of the zero sequence between circuit b and circuit c, is Yad；The mutual susceptance of zero sequence between circuit c and circuit d
Parameter is Ycd；
Measuring process includes：
Step 1, have a power failure and measure transmission line with four-circuit on single tower, four loop line road first and last end three-phases are distinguished into short circuit；Route survey includes：
Measurement method one：Circuit a head ends pressurize, end ground connection；Circuit b head ends are hanging, end ground connection；Circuit c head ends are hanging, end
End ground connection；Circuit d head ends are hanging, end ground connection；
Measurement method two：Circuit a head ends are hanging, end ground connection；Circuit b head ends are hanging, end ground connection；Circuit c head ends pressurize, end
End ground connection；Circuit d head ends are hanging, end ground connection；
Step 2, the sync identification function of GPS, synchro measure circuit a, circuit b, circuit c and circuit d are utilized
The residual voltage data and zero-sequence current data of head end and end；
Step 3, the residual voltage measurement data and zero sequence current measurement number to being obtained under each independent measurement method obtained by step 2
According to the zero sequence fundamental voltage phasor and zero sequence fundamental wave for obtaining head end and end under the independent measurement method using fourier algorithm are electric
Phasor is flowed, these phasor datas is recycled to solve the Zero sequence parameter of transmission line with four-circuit on single tower to come；
The parameter of required solution includes the zero sequence self-impedance parameter Z of unit length11、Z22, zero sequence mutual impedance parameter Zab、Zac、Zad、
Zcd, zero sequence is from susceptance parameter Y11、Y22, the mutual susceptance parameter Y of zero sequenceab、Yac、Yad、Ycd, then solved according to following two formula all
Zero sequence parameter：
Formula one
Formula two
Wherein, because the leakage current very little of circuit, does not consider conductance parameter；Quadri-circuit lines on the same tower road is defined as parallel erection
And length is all l, the zero sequence fundamental voltage phasor for defining tetra- back transmission line head end of a, b, c, d is respectively The zero sequence fundamental voltage phasor of end is respectivelyThe zero sequence fundamental wave electricity of head end
Flowing phasor is respectivelyThe zero sequence fundamental current phasor of end is respectively
Zero sequence parameter solution procedure is as follows：
Step 3.1, by Zero sequence parameter Z11、Z22、Zab、Zac、Zad、ZcdAnd Y11、Y22、Yab、Yac、Yad、YcdObtain transmission line of electricity head
The relationship of terminal voltage electric current：
Wherein Aaa,Aab,Aba,Abb, Baa,Bab,Bba,Bbb,A′aa,A′ab,A′ba,A′bb, B 'aa,B′ab,B′ba,B′bbIt is and circuit
The intermediate variable of relating to parameters；
Formula three
Formula four
Step 3.2, intermediate variable A is calculated by two kinds of measurement methods in step 1aa,Aab,Aba,Abb, Baa,Bab,Bba,Bbb,
A′aa,A′ab,A′ba,A′bb, B 'aa,B′ab,B′ba,B′bb：
Formula five
Formula six
Formula seven
Formula eight
In the above formulas, voltage phasor or electric current phasor with subscript " 1 " or " 2 ", indicate the phasor be connections mode 1 or
The zero sequence fundamental voltage phasor or zero sequence fundamental current phase that measurement data under the mode of connection 2 is calculated through Fourier algorithm
Amount；
Step 3.3, characteristic root p is calculated according to following formula1,p2,p′1,p′2；
Formula nine
Formula ten
Then pass through p1,p2,p′1,p′2Solve A1,A2,B1,B2And A '1,A′2,B′1,B′2；
Formula 11
Formula 12
Step 3.4, by Aaa,Aab,Aba,Abb,A′aa,A′ab,A′ba,A′bbSubstitute into following formula calculating matrix T1And T3；
Formula 13
Formula 14
Step 3.5, B is substituted intoaa,Bab,Bba,Bbb,B′aa,B′ab,B′ba,B′bbWith matrix T1、T3Computing impedance matrix Z1、Z2；
Formula 15
Formula 16
Step 3.6 is by matrix T1、T3、Z1、Z2Following formula is substituted into, zero sequence admittance matrix is calculated；
Formula 17
Formula 18
Step 3.7, zero sequence impedance and zero sequence admittance parameter are calculated；
Formula 19
Formula 20
Formula 21
Formula 22
Finally, by Z11、Z22、Zab、Zac、Zad、ZcdAnd Y11、Y22、Yab、Yac、Yad、YcdObtain corresponding transmission line with four-circuit on single tower
Zero sequence resistance, zero sequence inductance, zero sequence capacitance parameter；
Wherein, symbol sh () indicates that hyperbolic sine function, symbol ch () indicate hyperbolic cosine function, symbol arch () table
Show that Inverse Hyperbolic Cosine Function, the π of ω=2 f, f are power system frequency 50Hz, l indicates quadri-circuit lines on the same tower road length.
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